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Multiplication Operators Between the Lipschitz Space and the Space of Bounded Functions on a Tree

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Abstract

In this paper, we characterize the bounded and the compact multiplication operators between the space of bounded functions on the set of vertices of a rooted infinite tree T and the Banach space of complex-valued Lipschitz functions on T. We also determine the operator norm and the essential norm for the bounded multiplication operators between these spaces and show that there are no isometries among such operators.

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Authors and Affiliations

  1. George Mason University, Fairfax, Virginia, U.S.A.

    Flavia Colonna

  2. System Planning Corporation, Arlington, Virginia, U.S.A.

    Glenn Easley

Authors
  1. Flavia Colonna
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  2. Glenn Easley
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Correspondence to Flavia Colonna.

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In memory of Walter Rudin

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Colonna, F., Easley, G. Multiplication Operators Between the Lipschitz Space and the Space of Bounded Functions on a Tree. Mediterr. J. Math. 9, 423–438 (2012). https://doi.org/10.1007/s00009-011-0131-y

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  • DOI: https://doi.org/10.1007/s00009-011-0131-y

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